![Page 1: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/1.jpg)
STM imaging of broken symmetry statesin cuprate superconductors
Jinsheng WenZhijun XuGenda Gu
Brookhaven
Ilija ZeljkovicLiz Main
Tess WilliamsYi Yin
Martin ZechJenny Hoffman
STM Experiments:
Thanks to:
Michael BoyerKamalesh Chatterjee
Doug WiseEric Hudson
Harvard Physics
Bi-2212 Samples:
Takeshi KondoT. Takeuchi
Hiroshi IkutaNagoya University
Bi-2201 Samples:MIT Physics
![Page 2: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/2.jpg)
Hoffman Lab STM (9T v, 3T h; 1-40K)
Hoffman Lab UHV STM(9T v, 3T h; 2-80K)
Bi-2201 Ba-122 ironpnictide
topologicalinsulator
Hoffman/Hudson Lab Local Probes
Bi-2212NbSe2
Hudson Lab UHV STM(4-120K)
Bi-2212Bi-2201 Sr-122 ironpnictide
![Page 3: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/3.jpg)
Cuprate Phase Diagram
x (doping)
B
T
3-dim cuprate phase diagram
doped Mott insulatorbecomes metal
antiferromagneticinsulator
energy (meV)
dens
ity o
f sta
tes
Boy
er, N
at P
hys
(200
7) Ordinarily:If lowering T opens a gap,this means some symmetry has been broken.→ Look for broken symmetry!
Problem:Cuprates are disordered…→ no obvious long-range electronic symmetry
breaking was initially seen experimentally
Theorists propose: hidden broken symmetries!
d-wavesuperconductor
energy (meV)
dens
ity o
f sta
tes
![Page 4: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/4.jpg)
Varma: sub-unit-cell orbital ordering
Underdoped cuprates havea hitherto undetectedbroken symmetry phasewhich does not breaktranslation symmetry.
The non-Fermi liquid “normal”state is the quantumcritical regime, in whichorder parameter fluctuationsstrongly scatter the quasiparticles.
The critical fluctuations “mediate”d-wave pairing.
Breaks time-reversaland inversion
but not the produce of TI.
![Page 5: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/5.jpg)
Kivelson, Fradkin: stripy liquid crystal phases
Kivelson, Fradkin, and Emery, Nature 393, 550 (1998).
Fluctuating stripes play to role of the “nematogens” which allowsfor the formation ofvarious “electronic liquid crystalline phases” in thepseudo-gap regime.
Local stripe order may enhancepairing, but stripe ordercertainly suppressessuperfluid stiffness.
Nematic:breaks long-range rotation
Smectic:breaks long-range rotation & translation
![Page 6: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/6.jpg)
Nayak & Chakravarty: d-density waveChakravarty, Int. J. Mod. Phys.
B 15, 2901 (2002)
Breaks time reversal and translational symmetry, but
preserves the product.
The pseudo-gap has broken translational symmetry and a correspondingpartial gapping and restructuring of the FS.
The order parameter is “hidden” in the sense that it is intrinsically difficult to see directly in experiment.
incommensurate,T-preserving
Nayak, PRB 62, 4880 (2000)
![Page 7: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/7.jpg)
Some broken symmetry states in the pseudo-gap (for which there is direct experimental evidence):
Electron Nematic: Uniform (translation symmetry unbroken)Fluid (metallic or superconducting)With spontaneously broken point group symmetry
(e.g. electronic orthorhombicity)
Electron smectic: Unidirectional metallic (or superconducting)charge density wave
Stripe phase: Unidirectional colinear spin density wave withcoexisting CDW with ½ the wavelength (Both insulating and conducting versions)
In the presence of weak disorder, this becomes a “clusterspin-glass” with only short-range stripe order.
Intra-unit cell antiferromagnet: Breaks time-reversal and somepoint-group symmetries (Chandra’s-loops)
d-density wave: Breaks time reversal and translational symmetry,but preserves the product.
slide stolen from Steve Kivelson!
![Page 8: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/8.jpg)
Lots of candidates for pseudogap from STM
x (doping)
B
T
3-dim cuprate phase diagram
antiferromagneticinsulator
d-wavesuperconductor
“Nematic” and “Smectic”
“Fluctuating Stripes”
Parker, Nature (2010)
Lawler, Nature (2010)
Electronic cluster glassCDW
Kohsaka, Nature (2008)Wise, Nat Phys (2008)
![Page 9: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/9.jpg)
? Structural →Electronic ?
Bi-2212 Bi-2201, Pb-doped another Bi-2201, Pb-doped
![Page 10: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/10.jpg)
Raw data(Bi-2201, Tc=32K, slightly underdoped)
QxQy
?
??
?
?
Bragg peaks are blurred → need to apply Lawler algorithm to dri -correct!
66x66 nm2
![Page 11: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/11.jpg)
Drift-corrected data(Bi-2201, Tc=32K, slightly underdoped)
QxQy
?
??
?
?
Bragg peaks sharpen up → they are true structureMost other peaks broaden out → they are noise
![Page 12: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/12.jpg)
Raw data(Bi-2201, Tc=32K, slightly underdoped)
QxQy
?
center pix only 20% brighter than nearest neighbors
![Page 13: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/13.jpg)
Drift-corrected data(Bi-2201, Tc=32K, slightly underdoped)
QxQy
Qb
center pix > 5x brighter than nearest neighbors
![Page 14: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/14.jpg)
Drift-corrected data(Bi-2201, Tc=32K, slightly underdoped)
QxQy
Qb
noisenoise
noise
noise
![Page 15: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/15.jpg)
Drift-corrected data(Bi-2201, Tc=32K, slightly underdoped)
QxQy
Qb
> 10x brighter than neighboring pixels
![Page 16: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/16.jpg)
Make Average Unit CellPixel gridexact tip location when data acquired
Bi atom
Note: data acquisition only slightly betterthan Nyquist frequency for atoms!
Make a new grid, one unit cell,but with more pixels than we have in raw data.
a0
Center Bi in center of this unit cell.
![Page 17: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/17.jpg)
Make Average Unit CellPixel gridexact tip location when data acquired
Bi atom
Note: data acquisition only slightly betterthan Nyquist frequency for atoms!
Make a new grid, one unit cell,but with more pixels than we have in raw data.
a0
Center Bi in center of this unit cell.
Build up a histogram of weight at each sub-unit-cell-resolved location.
![Page 18: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/18.jpg)
Make Average Unit CellPixel gridexact tip location when data acquired
Bi atom
Note: data acquisition only slightly betterthan Nyquist frequency for atoms!
Make a new grid, one unit cell,but with more pixels than we have in raw data.
a0
Center Bi in center of this unit cell.
Build up a histogram of weight at each sub-unit-cell-resolved location.
![Page 19: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/19.jpg)
Make Average Unit CellPixel gridexact tip location when data acquired
Bi atom
Note: data acquisition only slightly betterthan Nyquist frequency for atoms!
Make a new grid, one unit cell,but with more pixels than we have in raw data.
a0
Center Bi in center of this unit cell.
Build up a histogram of weight at each sub-unit-cell-resolved location.
![Page 20: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/20.jpg)
Make Average Unit CellPixel gridexact tip location when data acquired
Bi atom
Note: data acquisition only slightly betterthan Nyquist frequency for atoms!
Make a new grid, one unit cell,but with more pixels than we have in raw data.
a0
Center Bi in center of this unit cell.
Perfect registry allows sub-unit-cell resolution!
Build up a histogram of weight at each sub-unit-cell-resolved location.
![Page 21: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/21.jpg)
Make Average Unit Cell(Bi-2201, Tc=32K, slightly underdoped)
make averageunit cell
tile 4x4
66x66 nm2
![Page 22: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/22.jpg)
Make Average Unit Cell(Bi-2201, Tc=32K, slightly underdoped)
make averageunit cell
fit to make sure Bi is at center, where we think it should be
![Page 23: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/23.jpg)
Make Average Supercell: 2x2(Bi-2201, Tc=32K, slightly underdoped)
tiled
fit
shift by ~1% of unit cell
![Page 24: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/24.jpg)
Make Average Supercell: 4x2(Bi-2201, Tc=32K, slightly underdoped)
tiled
fit
![Page 25: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/25.jpg)
Make Average Supercell: 4x4(Bi-2201, Tc=32K, slightly underdoped)
tiled
fit
16 inequivalent sites:average displacement: 1.1%standard deviation: 0.36%
(error bar ~1/3 of effect → inconsistent with zero)
![Page 26: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/26.jpg)
Crystal Structure
CuO2
CuO2
BiO
BiO
SrO
SrO
Ca
CuO2
CuO2
BiO
BiO
SrO
SrO
Ca
Bi2Sr2CaCu2O8
ab
QX
QY
tetragonal BZ
![Page 27: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/27.jpg)
Crystal Structure
CuO2
CuO2
BiO
BiO
SrO
SrO
Ca
CuO2
CuO2
BiO
BiO
SrO
SrO
Ca
Bi2Sr2CaCu2O8
ab
QX
QY
tetragonal BZ
orthorhombic BZ
![Page 28: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/28.jpg)
Crystal Structure
CuO2
CuO2
BiO
BiO
SrO
SrO
Ca
CuO2
CuO2
BiO
BiO
SrO
SrO
Ca
Bi2Sr2CaCu2O8
ab
QX
Qa
QY
no Qb tetragonal BZ
orthorhombic BZ
a-axis modulation(π/2 phase)
![Page 29: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/29.jpg)
Back to q-space: does it check out?
Qb
![Page 30: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/30.jpg)
Apply 2 methods to many samples
QY
QX
Qa
QSM
No Qb
QY
QXQa
No Qb
QY
QXQa
No Qb
Zeljkovic, arxiv:1104.4342
![Page 31: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/31.jpg)
8 different Bi-2212 samples
QY
QX
Qa
QSM
No Qb
QSM ≡ crystalline b axis
8 samples: ortho distortion along a axis
mirror plane always chooses this axis
![Page 32: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/32.jpg)
Bi-2201 throughout the SC dome
0.05 0.10 0.15 0.20 0.25 0.300
1
2
3
4
Shift
(% O
rtho
Uni
t Cel
l)
Doping (p from TC)
0
5
10
15
20
25
30
35
40
TC (K
)
0 6 12 18 240.0
0.4
0.8
1.2
Shift
(% O
rtho
Uni
t Cel
l)
Temperature (K)
TC =15 K dc
Zeljkovic, arxiv:1104.4342
0 3 6 90.0
0.4
0.8
1.2
Shift
(% O
rtho
Uni
t Cel
l)
Magnetic field (T)
b
00.1
0.20.3
0
5
10
15
30
10
20
40
50
B (T)
T (K)
a
![Page 33: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/33.jpg)
Historical: Structure from Scattering
Material Pb? Technique Bi distortion Cu distortion Ref
Bi-2223 no XRD 2.22% (b axis) -0.01% (b axis) Subramanian, Science (1988)
Bi-2201 no XRD 2.58% (b axis) none Torardi, PRB (1998)
Bi-2212 no neutrons 2.55% (a axis) -0.07% (a axis) Miles, Physica C (1998)
Bi-2201 yes XRD 1.82% (a axis)6.34% (b axis)
none Ito, PRB (1998)
Bi-2212 yes XRD 1% (a axis)1.65% (b axis)
2.57% (a axis)-0.02% (b axis)
Calestani, PhysicaC (1998)
Bi-2212 yes XRD 1.1% (a axis)1.53% (b axis)
0.08% (b axis) Gladyshevskii, PBR (2004)
Bi-2201 yes and no
LEED, ARPES
one axis only can’t determine Mans, PRL (2006)
![Page 34: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/34.jpg)
STM adds: LOCAL symmetry determination
Qa
Qb
Qa
Qb
Zeljkovic, arxiv:1104.4342
ab
Bi-2201: Tc=25K, UD
ab
local mirror planes!
![Page 35: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/35.jpg)
Historical: Structure from Scattering
Material Pb? Technique Bi distortion Cu distortion Ref
Bi-2223 no XRD 2.22% (b axis) -0.01% (b axis) Subramanian, Science (1988)
Bi-2201 no XRD 2.58% (b axis) none Torardi, PRB (1998)
Bi-2212 no neutrons 2.55% (a axis) -0.07% (a axis) Miles, Physica C (1998)
Bi-2201 yes XRD 1.82% (a axis)6.34% (b axis)
none Ito, PRB (1998)
Bi-2212 yes XRD 1% (a axis)1.65% (b axis)
2.57% (a axis)-0.02% (b axis)
Calestani, PhysicaC (1998)
Bi-2212 yes XRD 1.1% (a axis)1.53% (b axis)
0.08% (b axis) Gladyshevskii, PBR (2004)
Bi-2201 yes and no
LEED, ARPES
one axis only can’t determine Mans, PRL (2006)
In the absence of supermodulation, there can be twin boundaries→ leads to the appearance of shi s along 2 axes
![Page 36: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/36.jpg)
Conclusions1. structural distortion in BiO plane breaks inversion
symmetry at the Bi site, but preserves mirror plane
ab
4. resolve long discrepancies in the bulk scattering literature:• supermodulated samples → no ortho twinning;• Pb-doped samples → can have ortho twinning
2. mirror plane is always aligned with supermodulation
Qa
Qb
3. can image the local mirror plane
00.1
0.20.30
5
10
15
30
10
20
40
50
B (T)
T (K)5. orthorhombic distortion present across large regions of
Bi-2201 phase diagram
![Page 37: STM imaging of broken symmetry states in cuprate](https://reader030.vdocuments.mx/reader030/viewer/2022012410/616a572211a7b741a3516d77/html5/thumbnails/37.jpg)
Implications1. Algorithms: we extend Lawler’s algorithm for 4 additional purposes
a. discriminating between noise (broadens) and signal (sharpens)b. make average unit cell: can arbitrarily exchange large area for high resolutionc. make average supercell: can detect any commensurate modulationd. use Fourier methods to locally track any structural modulation
2. Structural vs. electronic:a. We also see inversion “symmetry breaking” in the electronic signal.
It appears larger than structural, but we haven’t found a way to makeourselves confident that it is not a normalization artifact.
b. Investigations of local electronic “symmetry breaking” should take care to state which structural symmetries are already broken, and to compare the magnitudes of electronic and structural symmetry breaking.
c. If electronic “symmetry breaking” states just reinforce structural symmetries, but can be shown to follow T* line, then of course they are important and interesting.